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Dirac measures can be quantum limits on the Sierpinski gasket
Abstract
We prove that on the Sierpinski gasket, a prototype of compact fractal space, Dirac distributions arise as the weak limit of probability measures associated with sequences of high energy eigenfunctions of the Laplacian in a way that cannot happen in compact Riemannian manifolds.
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BibTeX
@misc{ruiz2026dirac,
title = {{Dirac measures can be quantum limits on the Sierpinski gasket}},
author = {Patricia Alonso Ruiz and Nikolay Tzvetkov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31200},
eprint = {2609.31200},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31200},
}
RIS
TY - UNPB
TI - Dirac measures can be quantum limits on the Sierpinski gasket
AU - Patricia Alonso Ruiz
AU - Nikolay Tzvetkov
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31200
UR - https://arxiv.org/abs/2609.31200
AB - We prove that on the Sierpinski gasket, a prototype of compact fractal space, Dirac distributions arise as the weak limit of probability measures associated with sequences of high energy eigenfunctions of the Laplacian in a way that cannot happen in compact Riemannian manifolds.
ER -